M 28/2.8 cleaning

Hi, I just bought a M 28/2.8. It is very sharp but lacks some constrast, and blown lights «contaminate» other parts. Here is a crop in a comparison I made between the M28 (left) and the DAL 18-55 (right):

There seems to be haze on inside lenses and I thought it would be good to open the lens to clean it.

But I couldn't go further than removing the focusing ring. It looks like that (without the ring):

I unsuccessfluly tried to turn the center parts with a metallic tool (and I didn't want to broke the lens…). some screws and a ring were glued, I wonder if it is the same for these parts. So do you know how to disassemble the lens further? Or it is a bad idea to do that?

I've been through that too - in my opinion it's not worth disassembling it if there isn't something obviously degrading the image quality. My copy has slow aperture blades during winter, and the rear element is badly scratched, but still it takes beautiful pictures. That comparison you made is kind of irrelevant, because the camera also does artificial corrections for the kit lens, while for manual lenses it does not. The high-contrast scene also does not do justice to any lens or digital camera [avoid windows when shooting indoors]. Shooting in raw and using an application to bump up your contrast is a wiser thing to do.
That being said, here's a picture I took yesterday using the 28mm.

Hello Fschhh, Welcome to the Forum!
I agree with Kcobain, stop before you do some serious damage to the lens.
I'd put it back together and try a couple of things. First, were you using a lens hood on the 28mm? Mine is very prone to flare and low contrast without one.
If you're sure the lens needs repair, send it to Eric;Home
And he'll give you an estimate.
Good Luck!
Ron